Mathematical Sciences: Research in Algebra and Algebraic Number Theory

这个项目是关于动机和动机的研究。 上同调 首席研究员会继续他的研究 他对动机的新定义的各种性质， 知识上同调 给定环上的任何拟投射概型X， 代数闭域k，X的Suslin复形应该给出 X作为派生范畴中的宾语的混合动机 阿贝尔群 首席研究员已经表明， 这是X的一个非常自然的定义，一条关于k的任意曲线， 他将研究曲面的情况。 另外他还会 调查他的广义定义的程度 Suslin复形可以被证明满足所需的公理。 本研究涉及代数K理论。 中 广义代数K-理论涉及概念的演化 从线性代数，如基础和向量空间。 这项工作 对数论和代数几何的重要影响， 并承诺在一些 不同的数学领域。

This project is concerned with research on motives and motivic cohomology. The principal investigator will continue his research in the various properties of his new definitions of motives and notivic cohomology. Given any quasiprojective scheme X over an algebraically closed field k, the Suslin complex of X should give the mixed motive of X as an object in the derived category of abelian groups. The principal investigator has already shown that this is a very natural definition for X an arbitrary curve over k, and he will investigate the case of surfaces. In addition, he will investigate the extent to which his generalized definition of the Suslin complex can be shown to satisfy the desired axioms. This research is concerned with algebraic K-theory. In a broad sense algebraic K-theory concerns th evolution of concepts from linear algebra such as basis and vector space. This work has significant implications for number theory and algebraic geometry, and promises to make exciting connections between a number of different areas in mathematics.